Session M3: Atomtronics and Vorticity

Finite--temperature effects in stirred ring Bose--Einstein condensates

A ring Bose--Einstein condensate (BEC) with zero circulation ($m=0$) stirred by a barrier will eventually jump to an $m=1$ state when stirred faster than a certain critical speed, $\Omega_{c}^{+}$. A ring BEC with $m=1$ will drop to $m=0$ when stirred at a critical speed, $\Omega_{c}^{-}$, which is lower than $\Omega_{c}^{+}$. The loop areas, $\Omega_{c}^{+}-\Omega_{c}^{-}$, of this hysteretic response of the BEC to stirring predicted by zero--temperature Gross--Pitaevskii equation (GPE) disagreed significantly with the results of a recent experiment. In the work reported here, we simulated this experiment with the phenomenologically damped GPE, [S. Choi, S. A. Morgan, and K. Burnett, Phys.\ Rev.\ A {\bf 57}, 4057 (1999)], and with the Zaremba--Nikuni--Griffin (ZNG) theory. The ZNG theory can account for finite--T, non--equilibrium dynamics. We compare the results of these simulations with the experimental data. The simulations show that a vortex/antivortex pair forms in the barrier region during the stirring and that this drives the hysteresis. We also show how the presence of an interacting, thermal cloud affects the dynamics of these pairs. We also simulate a ring condensate stirred by two barriers and find that the GPE matches the data much more closely.   

Interferometric measurement of the sign and magnitude of a persistent, quantized current in a BEC

We introduce a new method to simultaneously determine the sign and magnitude of a persistent, quantized current state of a ring-shaped BEC by interfering it with a phase reference. We implement this scheme by trapping neutral $^{23}$Na atoms in an all optical ``target trap shaped" potential, which consists of a disc surrounded by a toroidal trap. Previous experiments done in our group and elsewhere have measured the persistent current state of a ring-shaped BEC by observing a hole appear in the BEC after time of flight expansion [{\it Phys. Rev. Lett.}, {\bf 106}, 130401 (2011); {\it Phys. Rev. A.}, {\bf 86}, 013629 (2012)]. However, this method is unable to determine the direction of rotation. To overcome this limitation, we have added a disc-shaped trap inside the toroidal trap. The BEC trapped in the disc acts as an independent phase reference, which when released interferes with the BEC in the toroidal trap. The resulting atomic density distribution in time of flight has a spiral shape. The number of spiral arms gives the magnitude of winding number, while their chirality allows us to determine the direction of the persistent current.   

Measuring the current-phase relationship of a rotating weak link in a superfluid, quantized atomtronic circuit

We demonstrate a method of directly measuring the current-phase relationship of a weak link in a Bose-Einstein condensate formed into a closed atomtronic circuit. The current-phase relationship of a weak link that connects two superfluids (or superconductors) determines the transport properties and also dynamic effects such as phase slips or Shapiro steps. We create our circuit by combining a BEC of $^{23}$Na atoms shaped into a ring with a rotating constriction, i.e. a weak link. Due to the single-valued nature of the condensate wavefunction, such a closed circuit exhibits quantized flow. The behavior of the flow is analogous to the electrical current in an rf superconducting quantum interference device (SQUID). By interfering our ring with a phase reference (formed as a disc), we can measure the phase of the BEC in the ring. This phase information yields both the phase drop across the weak link and average current flowing around the ring, thus allowing for a measurement of the current-phase relationship.   

Detection of topological excitations in atom circuits via phase reference

Atom circuits (such as ring Bose--Einstein condensates [BECs]) can now be implemented in ultracold--atom systems confined in a horizontal plane with a red--detuned light sheet plus an essentially arbitrary two--dimensional potential in the plane. Atom--circuit operation may be effected by subsequent interaction with the system (such as stirring a ring BEC with a blue--detuned laser). These interactions will create topological excitations such as solitons, phonons, and ring-- and line--vortices which may be critical to circuit operation. It is therefore interesting to study methods by which such topological excitations can be detected and to identify the various signatures whereby the different excitations can be distinguished. We have investigated methods for doing this in multiply connected BECs in which part of the condensate participates in the atom circuit while another part is left alone so that its phase profile is undisturbed. By releasing the confinement and allowing different parts of the condensate to overlap the presence of these topological excitations may be detected via the resulting interference pattern. Using the time--depdendent Gross--Pitaevskii equation, we demonstrate ways in which this may be done for BECs in ring--ring and disk--plus--ring traps.   

Experimental realization of matter wave circuits

A matter wave circuit is a de Broglie wave analog of an integrated optical circuit where coherent matter waves are guided and manipulated by confining potentials. Applications of such circuits include sensing, quantum information processing, and emulation of transport problems. We report the experimental realization of matter wave circuits with the painted potential technique for creating arbitrary and dynamic time-averaged optical dipole potentials. First, a BEC was coupled into a straight waveguide and pushed to move with a chosen velocity. Second, the propagation of matter waves around bent waveguides was studied. Excitations were observed to be dependent on the radius of the bend. A simple theory explains this behavior and suggests ways to control the excitations. Third, a BEC was sent through a Y-junction and splitting of matter waves was shown. Dynamic control of the relative splitting ratio was demonstrated and the coherence between split matter waves was studied. Fourth, propagation of matter waves through a square closed waveguide was demonstrated. With these matter wave circuit elements, it is possible to construct matter wave interferometer circuits. Also the fine control of these elements may enable emulation of conduction problems in condensed matter systems.   

An atomtronic dumbell circuit

We report on simulations of the behavior of a Bose-Einstein condensate formed in the left well of a ``dumbell'' circuit potential. This quasi-2d potential takes the form of the combination of strong harmonic vertical confinement along with a horizontal-plane potential having dumbell shape. The dumbell consists of two circular wells connected by a channel. We assume that the condensate is initially formed in one of the wells and then is released and allowed to flow down the channel into the other well and possibly back again. We first simulated the behavior of the BEC in this potential using a variational mean-field version of the 3D Gross-Pitaevskii equation (GPE) at zero temperature for dumbell potentials having a range of different channel lengths and widths. We used these results to indentify equivalent ``atomtronic'' circuits such as an RCL circuit with DC battery. We also investigated the effects of finite temperature on the behavior of the condensate in the dumbell potential using the Zaremba-Nikuni-Griffin (ZNG) theory. These results were used to identify the effects of a thermal cloud on the atomtronic circuit operation.   

Energetic stability of coreless vortices in spin-1 Bose-Einstein condensates with conserved magnetization

We show that a coreless vortex can be energetically stable when phase-imprinted on a spinor Bose-Einstein condensate whose interactions favor the polar phase~[1], as prepared in recent experiments. Coreless vortices would in this case not be expected to occur by simple energetic arguments alone. The stabilizing mechanism instead arises from conservation of the prepared longitudinal magnetization, which causes mixing of phases. The stable vortex can then form a composite topological defect with distinct small- and large-distance topology: a hierachical core structure forms where an inner ferromagnetic coreless vortex continuously deforms toward an outer singular, singly quantized polar vortex. A similar mechanism can also stabilize a nonsingular nematic texture---a nematic coreless vortex---in the polar phase as the inner core of an outer ferromagnetic singular vortex. We describe the composite core by constructing a qualitative analytic model. Our results suggest that spinor condensates may act as laboratory emulators to shed light on the generic features of composite cores that appear also in, e.g., superfluid $^3$He and high-energy physics.\\[4pt] [1] J.~Lovegrove, M.~O.~Borgh and J.~Ruostekoski, Phys.~Rev.~Lett., in press, arXiv:1306.4700.   

Characterizing the momentum distribution of vortex systems in an expanded Bose-Einstein condensate

The quantization of the vorticity and the ease of experimental accessibility and control make Bose-Einstein condensates ideal systems to study the dynamics of disordered arrangements of vortices, or vortex tangles. Recently, the experimental generation of a vortex tangle in a cigar shaped BEC [1] has revealed that upon expansion the condensate maintains its aspect ratio, in contrast to the well-established inversion of aspect ratio for an elongated non-turbulent BEC. We investigate the requirements for this self similar expansion by numerically modelling the expansion of a BEC with various vortex configurations, including vortex lattices, array of vortex dipoles and vortex tangles. Furthermore, we calculate the momentum distribution [2] of these condensates, both before and during the expansion, with the aim to determine whether this quantity characterizes the vortex configuration in a reliable way.\\[4pt] [1] Henn et al. PRL 103, 045301 (2009).\\[0pt] [2] Thompson et al. Laser Phys. Lett. 11, 015501 (2014).   

Half-vortices in a Polariton Ring Condensate

We have observed a persistent current in a half-vortex state in a polariton ring condensate. The polaritons in our experiments are photons which are strongly renormalized as a result of a sharp electronic resonance in a medium embedded in a microcavity. These polaritons are approximately number conserved, and have a repulsive interaction and a small effective mass. Our method of trapping them in a ring is a new technique which combines a stress-induced harmonic potential and a laser-generated central barrier. This method enables fine control of the trap profile and as well as the properties of the polaritons in the trap. We directly observe the phase gradient of the persistent current of the condensate in the trap, and record the rotation of the superposition of the two spinor states around the vortex.